Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Krzysztof Retel**- University of Bialystok

- The paper introduces some preliminary notions concerning the graph theory according to [18]. We define Necklace $n$ as a graph with vertex $\{1,2,3,\dots,n\}$ and edge set $\{(1,2),(2,3),\dots,(n-1,n)\}.$ The goal of the article is to prove that Necklace $n$ and Complement of Necklace $n$ are isomorphic for $n = 0, 1, 4.$

- Preliminaries
- Auxiliary Concepts
- Necklace $n$

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Grzegorz Bancerek.
Cardinal numbers.
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Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Grzegorz Bancerek.
Sequences of ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Jozef Bialas.
Group and field definitions.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Basic functions and operations on functions.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Czeslaw Bylinski.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [14]
Czeslaw Bylinski.
Galois connections.
*Journal of Formalized Mathematics*, 8, 1996. - [15]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Adam Grabowski.
On the category of posets.
*Journal of Formalized Mathematics*, 8, 1996. - [17]
Shunichi Kobayashi.
Predicate calculus for boolean valued functions. Part XII.
*Journal of Formalized Mathematics*, 11, 1999. - [18] Stephan Thomasse. On better-quasi-ordering countable series-parallel orders. \em Transactions of the American Mathematical Society, 352(6):2491--2505, 2000.
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Andrzej Trybulec.
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*Journal of Formalized Mathematics*, 1, 1989. - [20]
Andrzej Trybulec.
Enumerated sets.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [22]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [23]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [25]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [26]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [27]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
*Journal of Formalized Mathematics*, 1, 1989.

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